The Kuramoto model with high-order coupling has recently attracted some attention in the field of coupled oscillators in order, for instance, to describe clustering phenomena in sets of coupled agents. Instead of considering interactions given directly by the sine of oscillators’ angle differences, the interaction is given by the sum of sines of integer multiples of these angle differences. This can be interpreted as a Fourier decomposition of a general -periodic interaction function. We show that in the case where only one multiple of the angle differences is considered, which we refer to as the “Kuramoto model with simple -order coupling,” the system is dynamically equivalent to the original Kuramoto model. In other words, any property of the Kuramoto model with simple higher-order coupling can be recovered from the standard Kuramoto model.
Skip Nav Destination
Article navigation
November 2019
Research Article|
November 25 2019
Dynamical equivalence between Kuramoto models with first- and higher-order coupling
Robin Delabays
Robin Delabays
1
School of Engineering, University of Applied Sciences of Western Switzerland
, CH-1950 Sion, Switzerland
2
Institut für Automatik, ETH Zürich
, CH-8092 Zürich, Switzerland
Search for other works by this author on:
Robin Delabays
1,2
1
School of Engineering, University of Applied Sciences of Western Switzerland
, CH-1950 Sion, Switzerland
2
Institut für Automatik, ETH Zürich
, CH-8092 Zürich, Switzerland
Chaos 29, 113129 (2019)
Article history
Received:
July 06 2019
Accepted:
November 11 2019
Citation
Robin Delabays; Dynamical equivalence between Kuramoto models with first- and higher-order coupling. Chaos 1 November 2019; 29 (11): 113129. https://doi.org/10.1063/1.5118941
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Introduction to Focus Issue: Data-driven models and analysis of complex systems
Johann H. Martínez, Klaus Lehnertz, et al.
Reservoir computing with the minimum description length principle
Antony Mizzi, Michael Small, et al.
Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology
Eugene Tan, Shannon Algar, et al.
Related Content
Clusterization and phase diagram of the bimodal Kuramoto model with bounded confidence
Chaos (September 2020)
Directed acyclic decomposition of Kuramoto equations
Chaos (September 2019)
Exploring the interplay of excitatory and inhibitory interactions in the Kuramoto model on circle topologies
Chaos (April 2024)
Multistability of phase-locking in equal-frequency Kuramoto models on planar graphs
J. Math. Phys. (March 2017)
Configurational stability for the Kuramoto–Sakaguchi model
Chaos (October 2018)